Back up on iTune/icloud with the 5 turn off find my iPhone then factory reset.
On the iPhone 6 during the setup process restore using backup.
First go to Settings/iCloud. Go down to Find My iPhone and turn that off.
Then go to Settings/General/Reset and select Erase All Content and Settings
After that it will be a fully erased iPhone in the state when it is bought new. It will not erase anything on your other phone.
IF you are using the same Apple ID, you do NOT want to back up to iCloud, which would over write the last backup from your iPhone 6 (when using the free 5 GB of backup storage, you have limits before the backup will fail.)
IF you want to keep data, like game progress on angry birds, nothing needs to be done other than make sure the name of the phone is different. "LK's iPhone 5" and "LK's awesome iphone 6".
you can turn off iCloud backup for the old phone in settings.
if there were pictures on the phone you want to recover, do not back up, but use Dropbox App to upload and then access on the new phone with Dropbox App also.
depending on what you want to do with the old phone, you could reset to factory, or sign your Apple ID out and put a new Apple ID on it.